Regulatory “stress tests” at 19 major banks have set the stage for the strongest banks to distinguish themselves from weaker ones, by returning government rescue funds.

The goal is simple: Bankers want to be free to run their own business without extra government oversight and the stigma that comes from being labeled as a recipient of funds from the so-called TARP (Troubled Asset Relief Program).

But where many financial firms want to pay the money back, not all have the means. What comes after the stress tests is a race by banks to prove they can fund themselves by turning to private investors.

Even banks that are being asked to raise their cushion of capital, as a result of the stress test, are angling to do so in a manner that doesn’t tether them more closely to the government. Bank of America, for example, needs to raise $34 billion in fresh capital, and it's planning to do that in a way that hastens the day when it can exit from TARP.

The moves would be good news in the view of most US taxpayers, who don’t want to fund Wall Street bailouts. A revival of marketplace funding for banks would also represent an important step toward normal functioning of credit markets – and the notion that firms should rise or fall on their merits.

Banks that are unable to win the confidence of the marketplace will remain tied closely to government support.

“Those banks which can end their dependence on federal guarantees will be the visible winners in the post stress test market,” says banking analyst Christopher Whalen of Institutional Risk Analytics, in a report issued Friday. The market value of firms “will reflect this divergence between zombies and viable private banks.”

The US Treasury does not use the word “zombie.” It has framed the stress review as a way of ensuring that all 19 firms have plenty of capital to survive and keep lending, even if the recession proves worse than anticipated.

The intensive review, conducted by several agencies including the Federal Reserve, showed that some financial firms are in much better shape than others. Regulators called for 10 banks to raise about $75 billion collectively in new capital, while nine were deemed well-capitalized to handle a tough economy through this year and next.

But just because a bank passed the test without a call to raise fresh capital doesn’t necessarily mean it will have an easy time paying back the capital that the Treasury has put in since last fall. Treasury Secretary Timothy Geithner wants banks to prove, before they can exit TARP, that they don’t need help from another government program – guarantees on their debts provided by the Federal Deposit Insurance Corp. (FDIC).

Still, the industry is clearly trying to put the stigma from the bailout, and the resulting scrutiny from Congress, behind it:

• Morgan Stanley is moving to raise $4 billion in bonds without the FDIC guarantee. The firm also plans to raise capital with a stock offering to private investors, in excess of the $1.8 billion called for by the stress test.

• American Express has formally requested permission to return its $3.4 billion in TARP money. “We've always viewed [the Treasury funding] as a temporary program, and we believe that repaying the investment at this time is not only in the best interest of American Express shareholders, but also good public policy,” CEO Kenneth Chenault said Thursday evening after the stress results.

• Several banks, from giant JPMorgan to US Bancorp and State Street, have announced the intent to pay back TARP funds. In many cases, the companies got the federal infusion not because they requested it, but because the Treasury wanted to provide assurance that banks had the necessary capital and support at a time of market turmoil last fall.

Bank of America, the firm asked to raise the most money by regulators, says it plans to do so by issuing stock privately or by selling some of its business, not by tapping the government for more capital.

“Our game plan,” said Ken Lewis, the bank's chief executive, is to “get the government out of our bank as quickly as possible.”

In addition to JPMorgan and Bank of America, the two other US megabanks are Citigroup and Wells Fargo. Wells, asked to raise $13.7 billion, plans to do that by offering new stock to investors and by setting aside earnings in the next few months.

Citigroup, asked to raise $5.5 billion, also plans to raise the money privately. Still, of all the big banks, Citi remains the most closely tethered to government support. The government is poised to own about one-third of the company, as the bank proceeds with a large previously announced plan to boost capital by converting TARP funds and private-investor money into common stock.

As some banks return funds to the government, it will add to the modest amount left from the original $700 billion of TARP funds – money available for potential needs in the months ahead. That means President Obama may not have to take the politically unpopular step of asking Congress for more money to rescue financial firms.

Still, the Obama banking strategy comes with risks, some economists say. If the economy performs worse than the stress test envisioned, some firms that pay back TARP money could end up undercapitalized, with too little seed money available for new lending. That would constrain an economic recovery.